Our ETL's are doing something similar but only to certain departments. And to TM's that do chat a lot, but they do also get A TON of work done and are excellent employees overall.
This is the advice I gave to those TM's (who are not my TM's, but they asked what they could do):
1. As they're listing what you're to be doing for the day, visibly write it down. By visibly I mean get a little notebook, write it down as they're talking. Let them see you're taking notes and being attentive to their requests. DO NOT use your phone.
2. After they're done listing, THANK THEM (I know, but seriously they'll love it) ask which tasks are the priority. Lately it's been ZONE first, reshop, then push. Even if it's repetitive, ask it.
3. Throughout your day, do the tasks. Say it took 30 minutes to zone, 20 to push reshop, then you pushed for an hour before your 15. Write all that down. At 2pm you got pulled to do 2 SFS carts? Write that down and also how long it took you. Take a pic of MPM stats when you're done. You had to backup at the lanes for 20 minutes at 4pm? Write that down.
Truly anything and everything you can think of to speak to your own personal volume of work and accomplishments. Keep the log so that if you do get pulled aside again by anyone, you have it and know exactly what you did. If they're still on you, go to the SD with your info. If all of the store's TM's are doing this and you're doing what you can, you're establishing a pattern to the SD that you're all doing what you can and then the SD can go to the ETL about why they're not supporting you.
As a TL in a store with a lot of new upper management, I do all of this too. Cover your butt always.
KEEP IN MIND. They can access reports for everything you're doing. Don't fudge the number like how long you had to look for items or how long you were at the lanes. While they can't coach from the cameras, they will likely check them.